Yeah, from Kouko's perspective, she thinks it's normal for a girlfriend to look through the mail of their significant other while they're away. Checking, not opening and peering over each one to see if Banri is having illicit correspondence with another woman, which she's always trying not to worry over
.
Y'know, after all the romantic troubles of Mitsuo and Kouko, and Banri and Linda, it was kinda refreshing to see the married couple that had been together since middle school. I guess Takemiya isn't
completely against childhood friends, or relationships relatively close to that level
.